Constructing $K-$optimal designs for different Scheff\'{e} models

TL;DR

This paper develops methods to construct $K$-optimal experimental designs specifically for first- and second-order Scheffé models, addressing a gap in mixture experiment design optimization.

Contribution

It provides the first analytical solutions for $K$-optimal designs in Scheffé models, enhancing design efficiency in mixture experiments.

Findings

Analytical solutions for first-order Scheffé models.

Analytical solutions for second-order Scheffé models.

Numerical examples demonstrating the effectiveness of the designs.

Abstract

To avoid multicollinearity in regression analysis, Ye and Zhou(2013) proposed $K-$optimality criterion. By far the most popular models for modeling the response of a mixture experiment are the Scheff\'{e} models. However, there have been no reports about constructing $K-$optimal designs for mixture models. The paper constructs $K-$optimal designs for first-order and second-order Scheff\'{e} models. The analytical solutions for first-order and second-order Scheff\'{e} models are obtained. A series of numerical results and examples are given to illustrate the theory.